2.1. Method overview

ArchIE2 is a method to detect introgressed tracts along an individual genome that can be applied in reference-free scenarios. ArchIE2 learns a direct mapping from genomic features to ancestry states, and as such, it requires labeled examples (genotypes of individuals annotated with segments of the genome annotated according to their introgression or ancestry state) for effective training which are generated using population genetic simulators.

The basic training workflow for ArchIE2 is as follows: First, a simulation program generates genotype data under a specified introgression scenario so that the genomes of individuals in the target populations are labeled with their tracts of introgression. Training ArchIE2 consists of two steps. The first step is feature generation, which takes the target and outgroup genotypes (ideally an outgroup that does not share the same introgression event) within each genomic window, combines them with the ground-truth ancestry labels, and produces a feature file for that window. The second step trains the ArchIE2 logistic regression model on this features file. Once trained, the same two-step workflow—feature generation followed by prediction—can be applied to estimate the probability of introgression for each individual genotype within a window. In practice, the demographic history underlying real data may differ from the simulation, but the model is assumed to be robust enough to handle such mismatches and still produce accurate predictions.

2.2. Feature design and model architecture

The ArchIE2 logistic regression model operates on features extracted from sliding 50kb windows on each haploid chromosome and produces the probability that each genotype within the window is introgressed (Figure 1). The length of 50kb is chosen to be sensitive to archaic introgression events in modern human history (since this is the expected length of introgressed tracts given an admixture time of around 2,000 generations before the present). To generate a SNP-based callset, we run ArchIE2 using a sliding window step size of 10kb, then calculate for each SNP the average probability of archaic ancestry across the five windows that span that SNP.

Figure 1. The ArchIE framework. Genetic data are processed into sliding windows, which are then fed into a logistic regression model, the resulting window based predictions are then averaged into SNP based predictions.

Eleven genomic features are used in ArchIE2, falling into two categories: those that require an unadmixed outgroup—a population that does not share the same introgression event as the target population—and those that do not. Among the outgroup-dependent features, ArchIE2 includes the minimum distance between the focal haplotype and the reference population, the number of private SNPs—i.e., SNPs unique to the target population—and the S^* statistic. Outgroup-independent features include the first four moments of the distance vector and the first four normalized moments of the individual frequency spectrum (IFS). The first four moments of the distance vector summarizes the length-N_target vector representing the Euclidean distance between the focal haplotype and each haplotype in the target population. The normalized first four moments of the IFS summarizes the length-N_target vector summarizing the allele frequency spectrum in the focal haplotype (e.g., counts of singletons, doubletons, etc.) (Table 1).

Table 1. Comparison of ArchIE vs ArchIE2 feature set and lengths.

2.3. Training and validation

3.1. Performance on simulated data

We developed ArchIE2 as a successor to ArchIE to address two limitations: (i) a dependence on sample-size dependent feature vectors, and (ii) the large number of correlated features, which increased the risk of overfitting and led to unstable coefficient estimates [18]. ArchIE2 addresses these issues by reducing the original high-dimensional set to 11 sample-size independent summary statistics, including the first four moments of the individual frequency spectrum (IFS) and the distance vector, along with features such as minimum distance, the number of private SNPs, and the S^* statistic. The mean and variance of the IFS are further normalized to account for sample-size effects (Table 1).

We compared ArchIE2 with ArchIE [18], the S^* statistic [7], and the HMMmix [14], using test data simulated under the same demographic history as the training scenario (Figure 2). Condensing the features of ArchIE2 produced virtually no loss in predictive accuracy compared to ArchIE, while yielding a more compact and interpretable model. ArchIE2 also outperformed both S^* and the HMMmix. These results indicate that ArchIE2 preserves the predictive strengths of its predecessor while mitigating instability and reducing feature complexity.

Figure 2. Precision-recall curves for various methods tested on data simulated with μ=1.25e-8.

3.2. Effect of sample size mismatch

Here we explore the flexiblity of ArchIE2 over ArchIE with respect to applicability across sample sizes. Here both ArchIE and ArchIE2 models were trained on the base Neanderthal introgression scenario with 100 European haplotypes, but were applied to a test set containing only 30 haplotypes. While ArchIE2 can handle this natively, ArchIE needs to be adapted to this setting. We consider two approaches to adapt ArchIE to this setting: 1) by padding the European genomes in the test set with genomes from a related population, for example Asians, so that the total sample size consists of 100 haplotypes or 2) duplicating genomes to reach the required sample size. ArchIE2 is more accurate than either approach to adapt ArchIE2 (Figure 3) illustrating the value of being able to naturally accommodate varying sample sizes.

Figure 3. Precision-recall curves for ArchIE and ArchIE2 under mismatch in sample size (100 haplotypes in the training data and 30 haplotypes in the test data).

3.3. Model robustness to domain shift

Given the variation of mutation rates in the human genome, we investigated whether ArchIE2 compares with other methods in response to shifts in mutation and recombination rates. We use the model trained under μ = 1.25e-8, r = 1e-8, and apply them to four scenarios: high vs. low mutation rate and high vs. low recombination rate. In application to real data, we would most probably utilize a single threshold when applying the models to the data. Therefore, we will also report the precision / recall with fixed thresholds for ArchIE and ArchIE2 in Table 2.

Table 2. Precision/recall values across scenarios. One threshold was chosen for each model corresponding to precision=0.8 in the base scenario, and we report its precision/recall in other scenarios while keeping thresholds fixed.

The effects of the change in mutation and recombination rates are consistent between ArchIE and ArchIE2 in Table 2. Low mutation rates and high recombination rates produce precision rates approaching one but very low recall, while high mutation rates and low recombination rates have opposite, albeit less extreme effects. The low recall under conditions of low mutation rates and high recombination rates is likely due to the scarcity of SNPs and the excessively short recombination segments produced.

Ethics Statement

Not applicable.

Consent for Publication

Not applicable

Availability of Data and Material

No new data were created or analyzed in this study. Data sharing is not applicable to this article

Funding

This work was supported by NIH grants GM125055, T32HGT002536, NSF grant CAREER-1943497.

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceptualization: H.W. and S.S.; Methodology: H.W. and S.S.; Software: H.W.; Validation: H.W.; Formal Analysis: H.W.; Investigation: H.W.; Resources: H.W.; Data Curation: H.W.; Writing – Original Draft: H.W.; Writing – Review & Editing: H.W. and S.S.; Visualization: H.W. ; Supervision: S.S.; Project Administration: H.W. and S.S.; Funding Acquisition: S.S.